The girl, identified as Sunnah on social media, and a 17-year-old boy died after getting into difficulty in the water next to Bournemouth Pier.
Eight others were pulled from the water on Wednesday but did not suffer serious injuries.
Police arrested a man in his forties who was “on the water” at the time on suspicion of manslaughter, but he has since been released under investigation.
A relative of the 12-year-old, who lived in High Wycombe, has now paid tribute, saying the family will remember her "every day for the rest of our lives".
“She was an absolute force of nature, liked by all and loved by so many,” The Times quotes a family member as saying. “She will be so sorely missed by her parents, siblings and friends.
“There are no words to describe the hole she has left in all of our hearts but we will remember her every day for the rest of our lives.”
Tributes have also flooded in on social media for the young girl. One friend said: “She was such an amazing person. She was so kind, caring, her smile lit up a room. It was far too early for our angel to gain wings.”
Another said: “She was basically my sister and I can’t believe it. Love you so much Sunnah.”
Eyewitnesses, including the father of one of the survivors, suggested this week that the swimmers had got caught up in a dangerous riptide.
Further reports from The Times suggest people on the lower levels of the pier ended up in the water after being caught in high waves.
Meanwhile, inspections and searches of a sightseeing boat at the centre of the investigation are still ongoing.
The Dorset Belle was impounded by police on Thursday afternoon.
On Friday the boat remained anchored at Cobb’s Quay, Poole Harbour, guarded by a police van.
Officials were seen on the boat on Friday continuing investigations into the vessel and any role it may have had in the incident.
According to the website Marine Traffic, the vessel had visited Bournemouth Pier, the scene of the incident, at 4pm, minutes before the first 999 calls were made, and returned again afterwards.
Dorset Police said no physical contact was made between the swimmers and any vessel or jet-ski and those involved had not been jumping off the pier.
A spokesperson for Bournemouth, Christchurch and Poole Council earlier said: “We do not license this boat.”
The authority’s website says: “Any person who wishes to be in charge or navigate a pleasure boat/vessel, including Poole Harbour and Christchurch Harbour, for the purpose of letting it out for hire to members of the public, or to be used for carrying passengers for hire, must obtain a licence from us.”
A council spokesperson added: “Concerning the Dorset Belle, the MCA [Maritime and Coastguard Agency] is responsible for issuing licences to operate vessels of this size and capacity.
“BCP Council does not issue licences for vessels of this nature to operate in open water.
“We apologise and acknowledge that the website doesn’t make this clear.”
Dorset Police have declined to comment on any investigation into the Dorset Belle and refused to say what or if any vessel was involved.
Tobias Ellwood, Conservative MP for Bournemouth East, has called on Dorset Police to provide more information to avoid “wild speculation”.
He said: “There needs to be a review, the police are conducting their investigation, there needs to be a review of the circumstances to see whether any safety measures and protocols need to be upgraded to ensure this doesn’t happen in the future.
“I encourage Dorset Police to clarify the general circumstances of this tragic accident to avoid further wild speculation and uncertainty for parents who may be cautious about going to any part of the beach, unclear of exactly what happened in this terrible incident.”
The vessel’s website states that it was purpose-built as a passenger boat to operate locally and could “cope with the occasional challenging swell conditions encountered at local piers”.
Bournemouth, Christchurch and Poole Council councillor Vicky Slade has said she will be discussing safety at the pier with local MP Conor Burns on Friday.
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